Seminars & Colloquia Calendar
2-Segal spaces and algebraic K-theory
Julie Bergner -- U.Virginia
Location: Hill 525
Date & time: Wednesday, 28 November 2018 at 2:00PM - 3:00PM
Abstract: The notion of a 2-Segal space was defined by Dyckerhoff and Kapranov and independently by Galvez-Carrillo, Kock, and Tonks under the name of decomposition space. Although these two sets of authors had different motivations for their work, they both saw that a key example is obtained by applying Waldhausen's S-construction to an exact category, showing that 2-Segal spaces are deeply connected to algebraic K-theory.
In joint work with Osorno, Ozornova, Rovelli, and Scheimbauer, we show that any 2-Segal space arises from a suitable generalization of this construction. Furthermore, our generalized input has a close relationship to the CGW categories of Campbell and Zakharevich. In this talk, I'll introduce 2-Segal structures and discuss what we know and would like to know about the role they play in algebraic K-theory.